Suppose that the earth will support a population of 16 billion people. According to the United Nations there were approximately 2 billion people in 1925 and 4 billion people in 1975. Let P(t) denote the population of the earth t years after 1925. Assume that human population growth follows the logistic model dP = kP(16 – P). dt (a) Find function P(t). (b) Use the logistic model to predict the population in 2020. (c) According to the model, during which year will the population reach 12 billion?

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Suppose that the earth will support a population of 16 billion people. According
to the United Nations there were approximately 2 billion people in 1925 and 4 billion people
in 1975. Let P(t) denote the population of the earth t years after 1925. Assume that human
population growth follows the logistic model
dP
= kP(16 – P).
dt
(a) Find function P(t).
(b) Use the logistic model to predict the population in 2020.
(c) According to the model, during which year will the population reach 12 billion?
Transcribed Image Text:Suppose that the earth will support a population of 16 billion people. According to the United Nations there were approximately 2 billion people in 1925 and 4 billion people in 1975. Let P(t) denote the population of the earth t years after 1925. Assume that human population growth follows the logistic model dP = kP(16 – P). dt (a) Find function P(t). (b) Use the logistic model to predict the population in 2020. (c) According to the model, during which year will the population reach 12 billion?
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